Related papers: A Tight Bound of Hard Thresholding
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \in {\mathbb R} ^n$ that has only $k \ll n$ non-zero coefficients from a small number $m \ll n$ of linear projections. The projections are…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…
Given an order-$d$ tensor $\tensor A \in \R^{n \times n \times...\times n}$, we present a simple, element-wise sparsification algorithm that zeroes out all sufficiently small elements of $\tensor A$, keeps all sufficiently large elements of…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
The problem of CSP sparsification asks: for a given CSP instance, what is the sparsest possible reweighting such that for every possible assignment to the instance, the number of satisfied constraints is preserved up to a factor of $1 \pm…
This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…